Eye-tracker with improved beam scanning and method therefor

ABSTRACT

The present disclosure describes systems and methods that enable eye-tracking by steering a light signal in a high-density Lissajous pattern over a region of an eye and detecting light reflected from the eye using a non-imaging photodetector configuration. The light signal is scanned by driving each axis of a two-axis MEMS scanner with a periodic signal having a frequency that is based on the resonant frequency of that axis. By choosing periodic signals having frequencies that give rise to precession of the Lissajous pattern at a high rate, a high-density scan pattern is quickly generated, thereby enabling eye tracking with high spatial resolution and low latency.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of co-pending U.S.Non-Provisional patent application Ser. No. 17/087,302, filed Nov. 2,2020 (Attorney Docket: 3001-006US2), which is a continuation of U.S.Non-Provisional patent application Ser. No. 15/876,148 (now U.S. Pat.No. 10,824,229), filed Jan. 20, 2018 (Attorney Docket: 3001-006US1),which claims the benefit of U.S. Provisional Patent Application Ser. No.62/448,577 filed Jan. 20, 2017, each of which is incorporated byreference as if set forth at length herein.

This application also claims the benefit of U.S. Provisional PatentApplication Ser. No. 62/957,696 filed Jan. 6, 2020 and U.S. ProvisionalPatent Application Ser. No. 63/134,467 filed Jan. 6, 2021, each of whichis incorporated by reference as if set forth at length herein.

If there are any contradictions or inconsistencies in language betweenthis application and one or more of the cases that have beenincorporated by reference that might affect the interpretation of theclaims in this case, the claims in this case should be interpreted to beconsistent with the language in this case.

TECHNICAL FIELD

This disclosure relates generally to human-computer interfaces and morespecifically to eye-tracking systems, methods and structures thatadvantageously provide rapid, high-accuracy measurements of eye positionwithout the need for time-consuming image processing.

BACKGROUND

The movement of the human eye can reveal a wealth of information aboutthe neural mechanisms of the brain and vision, as well as anindividual's neurological health, ocular health, interests, andstate-of-mind. In addition, the tracking of eye movement can be used toimprove/augment human-computer interaction, enable gaze-basedman-machine interfaces, and enhance how we interact with wearabletechnology. For example, gaze tracking, which relies on eye tracking,enables many augmentative alternative communication (AAC) devices thatimprove the ability for individuals lacking speech capability and/ormotor skills (e.g., amyotrophic lateral sclerosis (ALS) patients orthose with spinal cord injuries) to interact with the world around them.

Unfortunately, conventional eye-trackers are slow, bulky, invasive,and/or restrictive for the user. This makes them difficult, if notimpossible to use in many of the applications discussed above. Inaddition, conventional systems generally require cameras and imagingprocessing software. As a result, they tend to be expensive, slow, andpower hungry. Furthermore, they typically exhibit significant lagbetween eye movement and measured eye position, which degrades the userexperience in VR applications. It is possible to improve the resolutionand speed of such eye tracking systems but, to date, these improvementshave come at the expense of user mobility and added system cost.

Accordingly, systems, methods and structures that facilitate thedevelopment of low cost, precise eye tracking at a high rate wouldrepresent a welcome addition to the art.

SUMMARY

The present disclosure enables an eye tracker that scans a light signalin a two-dimensional scan pattern over a region of an eye and tracks themotion of the eye by detecting one or more reflections from the eye. Thescan pattern is configured to enable movement of the eye to be trackedwith low temporal latency and high spatial resolution.

An advance over the prior art is realized by scanning the light signalover the eye region in a Lissajous pattern that precesses at a high rateusing a two-axis, resonant MEMS scanner, where one axis is characterizedby a first resonant frequency and the other axis is characterized by asecond, different resonant frequency. Each axis is driven with aperiodic signal having a drive frequency that is near the resonantfrequency of that axis. The drive frequencies are selected to cause arapid precession of the pattern, which results in a high-density scanpattern in only a few periods of the drive frequencies.

An illustrative embodiment in accordance with the present disclosure isan eye-tracking system comprising a light source for providing anoptical signal, a two-axis, resonant MEMS scanner for steering theoptical signal in a scan pattern over a region of an eye, aphotodetector configuration that includes a non-imaging photodetector,and a processing system that is configured to drive each axis of thescanner with a periodic signal having a different drive frequency anddetermine a gaze vector of the eye based on the timing and amplitude ofthe light reflected from the region and detected by the photodetectorconfiguration.

The MEMS scanner includes a two-axis, gimbal-mounted mirror having firstand second orthogonal axes of rotation characterized by first and secondresonant frequencies, respectively. To scan the light signal over theeye region in a Lissajous pattern, the mirror is driven about the firstaxis by a first rotational actuator driven with a first periodic drivesignal having a first drive frequency based on the first resonantfrequency and about the second axis by a second rotational actuatordriven with a second periodic drive signal having a second drivefrequency based on the second resonant frequency. The first and seconddrive frequencies are selected to realize a Lissajous pattern thatprecesses at a rapid rate. In some embodiments, the MEMS scannerincludes a diffractive optical element (DOE) rather than a mirror.

In some embodiments, the photodetector configuration includes aplurality of photodetectors that is arranged such that each can receivereflections (e.g., specular reflections from the cornea, diffusereflections form the iris, etc.) from the eye region.

A method in accordance with the present disclosure includes determiningresonant frequencies for each axis of the scanner and developingcandidate drive frequencies by adding a small frequency offset to eachresonant frequency. Sets of test frequencies for the axes areestablished where each set is within a frequency range around itsrespective candidate frequency. Every combination of test frequenciesfor the two axes are then analyzed to determine the spatiotemporaldensity of a Lissajous formed using these frequencies for the drivesignals applied to the scanner. One test-frequency set is then selectedfor use in the drive signals for the scanner, where the test-frequencyset chosen is selected based on a scan pattern parameter, such asspatiotemporal density, the time required for the largest gap within thescan pattern to converge below a user-defined feature size, the size ofthe largest gap within the scan pattern at some user-defined scan time,the rate at which the scan pattern precesses, and the like.

An embodiment in accordance with the present disclosure is aneye-tracking method comprising: identifying a first location of a corneaof an eye, the cornea having a corneal surface; scanning a light signalin scan pattern over a region of the eye through the effect of amicroelectromechanical system (MEMS) device that is a two-axis devicehaving a first axis characterized by a first resonant frequency and asecond axis characterized by a second resonant frequency, wherein thescan pattern is a Lissajous pattern, and wherein the light signal isscanned by driving the first axis with a first periodic signal having afirst drive frequency and driving the second axis with a second periodicsignal having a second drive frequency; and detecting a first cornealglint reflected from the corneal surface with a non-imagingphotodetector configuration.

Another embodiment in accordance with the present disclosure is an eyetracker comprising: a light source for providing a light signal; ascanner for steering the light signal in a Lissajous pattern over aregion of an eye, wherein the scanner comprises a micromechanical system(MEMS) device that is a two-axis device having a first axischaracterized by a first resonant frequency and a second axischaracterized by a second resonant frequency; a non-imagingphotodetector configuration that is configured to provide at least oneoutput signal based on a reflected signal from the region; and aprocessing system configured to: (i) drive the first axis with a firstperiodic signal that is characterized by a first drive frequency; (ii)drive the second axis with a second periodic signal that ischaracterized by a second drive frequency; and (iii) determine a gazedirection of the eye based on the output signal.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a schematic block diagram illustrating an eye trackingsystem according to aspects of the present disclosure.

FIG. 2 depicts a schematic drawing of an exemplary operationaleye-tracking geometry for system 100.

FIG. 3 depicts a schematic drawing of a perspective view of a sourcemodule in accordance with the present disclosure.

FIG. 4 depicts a photo-illustration of a scanner in accordance withillustrative eye tracking system 100.

FIG. 5 depicts examples of Lissajous patterns generated by two-axisresonant scanners having different resonant frequency ratios.

FIG. 6 depicts operations of a method suitable for achieving a scanpattern having high spatial density and low latency in accordance withthe present disclosure.

FIG. 7 depicts plots showing representative sets of test frequencies fordriving axes A1 and A2 in accordance with the present disclosure.

FIGS. 8A-B depict a representative Lissajous pattern plotted in scanspace and phase space, respectively.

FIGS. 9A-B depict a representative Lissajous pattern plotted in scanspace and phase space, respectively, where the Lissajous pattern isgenerated using drive signal having a frequency ratio of 7:11.

FIG. 10 depicts a plot of D_(max)(i,j)[k] versus the number ofdrive-signal cycles, k, for a drive signal used to generate scanpatterns generated using two different sets of test frequencies.

FIG. 11 depicts a schematic drawing of an alternative operationaleye-tracking geometry in accordance with the present disclosure.

FIG. 12 depicts a series of timing diagram plots illustrating scanningin phase lock/resonance based optical feedback according to aspects ofthe present disclosure.

FIG. 13 depicts a plot of the detected pulses from photodetector module1102.

FIG. 14 shows a representation of the corneal glints as single points,as well as time series data corresponding to the pulses.

FIG. 15 depicts estimation of a gaze angle based on fused glintpositions.

FIG. 16 depicts pupil information and related glint information obtainedin accordance with the present disclosure.

FIG. 17 depicts an example of an eye-tracker-basedhuman-computer-interface in accordance with the present disclosure.

FIG. 18 depicts another eye-tracking-based user interface example inaccordance with the present disclosure.

FIG. 19 depicts yet another graphical-user interface that can be used toconfigure an avatar.

DETAILED DESCRIPTION

The following merely illustrates the principles of the disclosure. Itwill thus be appreciated that those skilled in the art will be able todevise various arrangements which, although not explicitly described orshown herein, embody the principles of the disclosure and are includedwithin its spirit and scope.

Furthermore, all examples and conditional language recited herein areprincipally intended expressly to be only for pedagogical purposes toaid the reader in understanding the principles of the disclosure and theconcepts contributed by the inventor(s) to furthering the art, and areto be construed as being without limitation to such specifically recitedexamples and conditions.

Moreover, all statements herein reciting principles, aspects, andembodiments of the disclosure, as well as specific examples thereof, areintended to encompass both structural and functional equivalentsthereof. Additionally, it is intended that such equivalents include bothcurrently known equivalents as well as equivalents developed in thefuture, i.e., any elements developed that perform the same function,regardless of structure.

Thus, for example, it will be appreciated by those skilled in the artthat any block diagrams herein represent conceptual views ofillustrative circuitry embodying the principles of the disclosure.Similarly, it will be appreciated that any flow charts, flow diagrams,state transition diagrams, pseudo code, and the like represent variousprocesses which may be substantially represented in computer readablemedium and so executed by a computer or processor, whether or not suchcomputer or processor is explicitly shown.

The functions of the various elements shown in the Drawing, includingany functional blocks that may be labeled as “processors”, may beprovided through the use of dedicated hardware as well as hardwarecapable of executing software in association with appropriate software.When provided by a processor, the functions may be provided by a singlededicated processor, by a single shared processor, or by a plurality ofindividual processors, some of which may be shared. Moreover, explicituse of the term “processor” or “controller” should not be construed torefer exclusively to hardware capable of executing software, and mayimplicitly include, without limitation, digital signal processor (DSP)hardware, network processor, application specific integrated circuit(ASIC), field programmable gate array (FPGA), read-only memory (ROM) forstoring software, random access memory (RAM), and non-volatile storage.Other hardware, conventional and/or custom, may also be included.

Software modules, or simply modules which are implied to be software,may be represented herein as any combination of flowchart elements orother elements indicating performance of process steps and/or textualdescription. Such modules may be executed by hardware that is expresslyor implicitly shown.

Unless otherwise explicitly specified herein, the figures comprising thedrawing are not drawn to scale.

FIG. 1 depicts a schematic block diagram illustrating an eye trackingsystem according to aspects of the present disclosure. As will beapparent to those skilled in the art by inspection of this figure, suchillustrative systems constructed according to aspects of the presentdisclosure exhibit substantial improvements in size, cost, powerconsumption, bandwidth and precision as compared with prior arteye-tracking systems.

In the depicted example, eye-tracking system 100 includes source module102, photodetector module 104, and processor 106, among other elements(e.g., memory, power module, etc.).

Source module 102 includes light source 108 and scanner 110.

Light source 108 is a conventional light source configured for providinga suitable light signal to scanner 110. In the depicted example, lightsource 108 provides a light signal having approximately 1 mW of opticalpower at 940 nm. The light signal has a Full-Width-at-Half-Maximum(FWHM) divergence of approximately 20 degrees, which is collimated andredirected toward scanner 110 by an Off-Axis-Parabola (OAP) that isintegrated in the package, as discussed below. After it reflects off theOAP, the light signal has a divergence of approximately 1-2 degrees. Itshould be noted, however, that light source 108 can be any of anyvariety known in the art without departing from the scope of the presentdisclosure.

Scanner 110 is a two-axis resonant MEMS scanning mirror that isconfigured to receive the light signal and scan it in a two-dimensionalscan pattern over a region of an eye being tracked. As discussed in moredetail below, scanner 110 includes first and second rotation axes, eachof which is characterized by a resonant frequency, and each of which isdriven with a periodic signal whose drive frequency is close to theresonant frequency of its respective axis. Emphasizing simple designprinciples according to the present disclosure, scanner 110 ispreferably a two-axis, resonant micro-electromechanical system (MEMS)device having two orthogonal rotation axes.

Photodetector module 104 includes one or more non-imaging photodetectorsconfigured to receive a portion of the light signal that is reflectedfrom the eye region and provide output signal 112 to processor 106. Inthe depicted example, photodetector module 104 includes a singlenon-imaging, discrete photodetector. For the purposes of thisdisclosure, including the appended claims, a “discrete detector” isdefined as an optoelectronic device having no more than fourelectrically independent detection regions on a single substrate, whereeach detection region is operative for providing one electrical signalwhose magnitude is based on the intensity of light incident upon thatdetection region. Examples of discrete detectors include detectorshaving only one detection region, split detectors having two detectionregions, four-quadrant detectors having four detection regions, andposition-sensitive detectors. The definition of discrete detectorexplicitly excludes individual pixels, or groups of pixels, within arraydevices for collectively providing spatially correlated imageinformation (i.e., imaging detectors), such as focal-plane arrays, imagesensors, and the like.

In some embodiments, photodetector module 104 includes multiplenon-imaging photodetectors that provide multiple output signals to theprocessor. Photodetector 104 can be any of any variety known in the artwithout departing from the scope of the present disclosure. Although thedepicted example includes a photodiode module having a singlephotodiode, in some embodiments, multiple photodiodes are used toprovide a richer data set for position of the eye.

As illustrated, processor 106 is communicatively coupled to scanner 110via a number of signal lines namely, pwr, V_(θ), V_(φ), V_(pd),V_(vcsel), and gnd, which correspond to electrical power, drivingvoltages (θ ϕ) for MEMS diffractive optic element, driving voltages forphotodetector and vertical cavity surface emitting laser (VCSEL) andground signals respectively. Note that for simplicity, individualelements comprising the module(s) are not specifically shown in thisillustrative figure namely, the MEMS scanning device, photodetector,VCSEL etc. Similarly, scanner 110 is communicatively coupled to lightsource 108 via pwr, gnd, and V_(pd) signals. As we shall show anddescribe, the modules containing the scanner and photodetector arelocated and operated a physical distance apart from one another.

Processor 106 is a controller/processor configured to drive thecomponents of source module 102 with appropriate drive signals, receiveoutput signal 112 from photodetector module 104, and generate anestimate of the gaze vector of an eye being monitored with system 100based on output signal 112, among other functions.

In some embodiments, processor 106 includes one or more componentscontaining processing and control circuitry that can include hardwarestructured to execute functions in accordance with the presentdisclosure. In some embodiments, such circuitry can includemachine-readable media for configuring the hardware to execute thefunctions described herein. Furthermore, the processing circuitry ofprocessor 106 can be embodied as one or more circuitry componentsincluding, but not limited to, processing circuitry, network interfaces,peripheral devices, input devices, output devices, sensors, etc. In someembodiments, such processing circuitry can take the form of one or moreanalog circuits, electronic circuits (e.g., integrated circuits (IC),application-specific integrated-circuits (ASICs), discrete circuits,system on a chip (SOCs) circuits, etc.), telecommunication circuits,hybrid circuits, and any other type of “circuit,” or combinationsthereof. In this regard, “processing circuitry” can include one or moreof any type of component for accomplishing or facilitating achievementof operations in accordance with the present disclosure. For example, acircuit as described herein can include one or more transistors, logicgates (e.g., NAND, AND, NOR, OR, XOR, NOT, XNOR, etc.), resistors,multiplexers, registers, capacitors, inductors, diodes, wiring, and soon).

“Processing circuitry” can also include one or more processors and/orcontrollers communicably coupled to one or more memory or memorydevices. In this regard, the one or more processors can executeinstructions stored in the memory or can execute instructions otherwiseaccessible to the one or more processors. In some embodiments, the oneor more processors can be embodied in various ways. The one or moreprocessors can be constructed in a manner sufficient to perform at leastthe operations described herein. In some embodiments, the one or moreprocessors can be shared by multiple circuits (e.g., circuit A andcircuit B can comprise or otherwise share the same processor which, insome example embodiments, can execute instructions stored, or otherwiseaccessed, via different areas of memory). Alternatively, oradditionally, the one or more processors can be structured to perform orotherwise execute certain operations independent of one or moreco-processors. In other example embodiments, two or more processors canbe coupled via a bus to enable independent, parallel, pipelined, ormulti-threaded instruction execution. Each processor can be implementedas one or more general-purpose processors, application specificintegrated circuits (ASICs), field programmable gate arrays (FPGAs),digital signal processors (DSPs), or other suitable electronic dataprocessing components structured to execute instructions provided bymemory. The one or more processors can take the form of a single coreprocessor, multi-core processor (e.g., a dual core processor, triplecore processor, quad core processor, etc.), microprocessor, etc. In someembodiments, the one or more processors can be external to theapparatus, for example the one or more processors can be a remoteprocessor (e.g., a cloud-based processor). Alternatively, oradditionally, the one or more processors can be internal and/or local tothe apparatus. In this regard, a given circuit or components thereof canbe disposed locally (e.g., as part of a local server, a local computingsystem, etc.) or remotely (e.g., as part of a remote server such as acloud-based server). To that end, processing circuitry in accordancewith the present disclosure can include components that are distributedacross one or more locations.

The present disclosure contemplates methods, systems and programproducts on any machine-readable media for accomplishing variousoperations. The embodiments of the present disclosure can be implementedusing existing computer processors, or by a special purpose computerprocessor and/or controller for an appropriate system, incorporated forthis or another purpose, or by a hardwired system. Embodiments withinthe scope of the present disclosure include program products comprisingmachine-readable media for carrying or having machine-executableinstructions or data structures stored thereon. Such machine-readablemedia can be any available media that can be accessed by a generalpurpose or special purpose computer or other machine with a processor.By way of example, such machine-readable media can comprise RAM, ROM,EPROM, EEPROM, CD-ROM or other optical disk storage, magnetic diskstorage or other magnetic storage devices, or any other medium which canbe used to carry or store desired program code in the form ofmachine-executable instructions or data structures and which can beaccessed by a general purpose or special purpose computer or othermachine with a processor. Combinations of the above are also includedwithin the scope of machine-readable media. Machine-executableinstructions include, for example, instructions and data which cause ageneral-purpose computer, special purpose computer, or special purposeprocessing machines to perform a certain function or group of functions.

FIG. 2 depicts a schematic drawing of an exemplary operationaleye-tracking geometry for system 100. Some eye-tracker system geometriesaccording to aspects of the present disclosure include a MEMS scannerthat sweeps a beam of light in a two-dimensional scan pattern over aregion of an eye (typically the region containing the cornea) and aphotodetector that receives light reflected from the region.

In the depicted example, source module 102 is mounted to temple 214 ofeyeglass frame 212, while photodetector module 104 is mounted to theframe 212 near bridge 216.

Light source 108 emits light signal 202, which is steered by scanner 110such that the light signal is scanned over scan region 206. In thedepicted example, scan region 206 includes cornea 208; however, in someembodiments, a scan region includes a different surface feature of theeye.

The scan pattern generated by source module 102 is based on drivesignals 218, which are provided by processor 106 to the rotation axes ofscanner 110. As discussed below in more detail, each axis of scanner 110is characterized by a resonant frequency and driven with a periodicsignal having a drive frequency that is based on that resonantfrequency. Those skilled in the art will appreciate that periodic drivesignals provided to each axis of scanner 110 gives rise to a scanpattern that is substantially a Lissajous curve (also known as aLissajous figure), which is the graph of a system of parametricequations defined by x=A sin(at+δ); y=B sin(bt).

Optical energy of light signal 202 is reflected from the surface ofcornea 208 at a glancing angle (˜60 degrees to the normal) ontophotodiode module 104 as reflected signal 210. As eye 204 rotates, theintensity of reflected signal 210 changes as a function of the positionof a unique point on cornea 208, thereby enabling a system according toaspects of the present disclosure to track position of this point and,as a consequence, the position of the cornea. Notably, the surface areaof the photodiode acts as a spatial filter to remove any highfrequencies from the far-field pattern projected by the scanner.

Photodetector module 104 detects reflected signal 210 and providescorresponding output signal 112 to processor 106, which generates anestimate of the gaze vector of the eye based on the output signal.

FIG. 3 depicts a schematic drawing of a perspective view of a sourcemodule in accordance with the present disclosure. Source module 102includes comprises source 108, OAP 302, and scanner 110.

OAP 302 is a reflective lens that is configured to reduce the FWHM oflight signal 112 and redirect it toward scanner 110 without significantloss. In some embodiments, OAP 302 is not included in source module 102.In some embodiments, source module 102 includes a flat mirror ratherthan an OAP.

FIG. 4 depicts a photo-illustration of a scanner in accordance withillustrative eye tracking system 100. Scanner 110 is a two-axis,resonant scanning mirror with two isothermal axes manufactured in in aCMOS process. When applied to such a device, CMOS-compatible voltagescan generate 90° (mechanical) deflections in both axes. As may beobserved from FIG. 4, the scanner geometry includes mirror 402 andactuators 404-1 and 404-2.

In the depicted example, mirror 402 is a substantially flatfirst-reflector surface formed on a structurally rigid plate that isoperatively coupled with actuators 404-1 and 404-2 to enable itsrotation about two orthogonal axes to steer light signal 202 in adesired pattern. Although the depicted example comprises a plane mirror,in some embodiments, scanner 110 includes a different optical element,such as a Fresnel zone plate as its optical element. As will be apparentto one skilled in the art, after reading this Specification, scanner 110can include any suitable optical element for steering a light signalwithout departing from the scope of the present disclosure. Examples ofalternative optical element suitable for use in accordance with thepresent disclosure include, without limitation, other diffractiveelements (e.g., holograms, Dammann gratings, etc.), refractive elements,lenses, and the like.

Each of actuators 404-1 and 404-2 comprises an opposed serpentinethermal-actuator pair that defines an axis of rotation and is configuredto impart rotation about its respective rotation axis. Actuator 404-1 isconfigured to impart rotation θ about rotation axis A1 in response todrive signal 218-1 from processor 106, while actuator 404-2 isconfigured to impart rotation ϕ about rotation axis A2 in response todrive signal 218-2 from processor 106. In the depicted example, scanner110 is configured such that actuator 404-1 scans light signal 202 in thehorizontal scan direction and actuator 404-2 scans light signal 202 inthe vertical scan direction.

The structure of actuator 404-1 defines resonant frequency f_(R1) forrotation axis A1, while the structure of actuator 404-2 defines resonantfrequency f_(R2) for rotation axis A2.

Operationally, to rotate the scanner reflector, the temperature of oneactuator is increased, while the opposed actuator's temperature isdecreased proportionally, thereby operating isothermally. In someembodiments, actuators 404-1 and 404-2 are driven with a singlepulse-width modulated (PWM) channel per axis, further simplifying itsoperation. In some embodiments, at least one actuator of a scanner isnot an isothermal actuator. In some embodiments, at least one ofactuators 404-1 and 404-2 comprises an actuator other than a thermalactuator, such as an electrostatic comb-drive actuator, parallel plateelectrostatic actuator, piezoelectric actuator, electromagneticactuator, and the like.

It should be noted that mirror 402 and actuators 404-1 and 402-2 aremerely exemplary and a wide range of and/or CMOS-MEMS actuators can beused in scanner 110 without departing from the scope of the presentdisclosure. Examples of alternative scanning elements and rotaryactuators suitable for use in accordance with the present disclosure aredescribed in detail in, for example, U.S. Pat. Pub. Nos. 20180210547,20150047078, 20160166146, and 20190204913, each of which is incorporatedherein by reference.

As will be apparent to one skilled in the art, the scan patterngenerated by a two-axis resonant system whose axes are driven at theirrespective (different) resonant frequencies can be modeled as asinusoidal function of time in each of its axes—referred to as aLissajous curve. Furthermore, one skilled in the art will recognize,after reading this Specification, that the shape and density of such acurve is determined primarily by the ratio between these resonantfrequencies.

FIG. 5 depicts examples of Lissajous patterns generated by two-axisresonant scanners having different resonant frequency ratios. Plots 500,502, and 504 show Lissajous curves generated by scanner 110 driven onresonance using drive signals 218-1 and 218-2 whose drive frequencieshave resonant frequency ratios of 1:1, 3:5, and 7:11, respectively, formultiple periods of the drive frequencies.

As would be apparent to one skilled in the art, each of the Lissajouscurves depicted in FIG. 5 constitutes a plurality of paths, each pathbeing traced during a different period (i.e., cycle) of the lowerfrequency of the pair of drive frequencies. As a result, many periodsthe drive signals are necessary to achieve a high-density pattern, suchas that shown in plot 504. Unfortunately, many eye-tracking applicationsrequire a high-density scan pattern that is generated at a high rate sothat eye movement can be tracked with low latency.

It should be noted that, since a Lissajous curve is defined via twoperiodic functions, a Lissajous pattern traced out over time (e.g., overmany cycles of the drive frequencies) will also be periodic if, and onlyif, the ratio between the drive frequencies of drive signals 218-1 and218-2 is a rational number.

Any Lissajous pattern of a given frequency ratio can be re-analyzed asbeing a precessing form of a different Lissajous pattern with a simplerrational frequency ratio. For example, a Lissajous pattern formed usinga drive-frequency ratio of 800:401 is substantially a precessing form ofa Lissajous pattern formed using a drive-frequency ratio of 2:1.However, the precession rate of such a pattern would normally be tooslow for use in many applications. It is an aspect of the presentdisclosure, however, that suitable drive frequencies can be identifiedusing methods analogous to that described below and with respect toFIGS. 6-9.

FIG. 6 depicts operations of a method suitable for achieving a scanpattern having high spatial density and low latency in accordance withthe present disclosure. Method 600 is described herein with reference tosystem 100 and continuing reference to FIGS. 1-4; however, methods inaccordance with the present disclosure are suitable for use with a widerange of two-axis resonant scanning systems.

Method 600 begins with optional operation 601, wherein resonantfrequencies f_(R) 1 and f_(R) 2 of axes A1 and A2, respectively, aredetermined. As will be apparent to one skilled in the art, the resonantfrequencies of axes A1 and A2 are dictated by the structure of actuators404-1 and 404-2. In some embodiments, f_(R) 1 and f_(R) 2 are measuredexperimentally. For example, in the depicted embodiment, a “ring-down”measurement is performed to determine the resonant frequency of each ofaxes A1 and A2. In some embodiments, processor 106 includes circuitryfor determining the resonance frequencies of the axes via an “in-system”ring-down procedure. In some embodiments, f_(R) 1 and f_(R) 2 areestimated based on the physical design of actuators 404-1 and 404-2.

At operation 602, candidate frequencies f_(c) 1 and f_(c) 2 areestablished for axes A1 and A2, respectively. In the depicted example,candidate frequencies f_(c) 1 and f_(c) 2 are established by addingfrequency offset FO1 to resonant frequency f_(R) 1 and frequency offsetFO2 to resonant frequency f_(R) 2.

At operation 603, a set of first test frequencies f_(T) 1(1) throughf_(T) 1(m) is established, where each first test frequency f_(T) 1(i)(for i=1 through m) is a frequency within a first frequency range, FR1,around candidate frequency f_(C) 1 such that the candidate frequency iswithin the first frequency range.

At operation 604, a set of second test frequencies f_(T) 2(1) throughf_(T) 2(n) is established, where each second test frequency f_(T) 2(j)(where j=1 through n) is a frequency within a second frequency range,FR2, around candidate frequency f_(C) 2 such that the candidatefrequency is within the second frequency range. In some embodiments, atleast one set of test frequencies includes the resonant frequency and/orcandidate frequency to which it corresponds.

In some embodiments, at least one of the sets of first and second testfrequencies is generated based, in part, on other system parameters,such as the structure of the electronics used to drive an actuator, oneor more reference clocks, capabilities of circuits included in processor106 (e.g., phase-lock loops, timers, etc.), and the like.

FIG. 7 depicts plots showing representative sets of test frequencies fordriving axes A1 and A2 in accordance with the present disclosure. Plot700 shows exemplary frequency components for the resonant frequencies,candidate frequencies, and sets of test frequencies for identifyingdesired drive frequencies for drive signals 218-1 and 218-2.

For each of i=1 through m and j=1 through n:

At operation 605, establish test-frequency pair (f_(T) 1(i), f_(T) 2(j))for drive signals 218-1 and 218-2.

At operation 606 determine the ratio, R(i,j), of the second testfrequency to the first test frequency test-frequency pair (f_(T) 1(i),f_(T) 2(j)), where R(i,j) is f_(T) 2(j):f_(T) 1(i).

At optional operation 607 generate a test scan pattern TSP(i,j) usingtest-frequency pair (f_(T) 1(i), f_(T) 2(j)) as drive signals 218-1 and218-2, respectively. In some embodiments, test scan pattern TSP(i,j) isgenerated by plotting it in phase space [ψ₁(i), ψ₂(j)], for a plurality,P, of cycles (i.e., periods) of drive signal 218-1, where 104 ₁(i) isthe phase of test frequency f_(T) 1(i) and ψ₂(j) is the phase of testfrequency f_(T) 2(j).

FIGS. 8A-B depict a representative Lissajous pattern plotted in scanspace and phase space, respectively. Plots 800 and 802 show a Lissajousscan overlaying an image of scan region 206, where the Lissajous scan isgenerated with drive signals 218-1 and 218-2 having a frequency ratio of3:5.

Plots 800 and 802 show Lissajous pattern 804 overlaying an image of ascan region, where the pattern and scan region are plotted in scan spaceand phase space, respectively.

As seen from plot 800, Lissajous pattern 804 is highly complex whenplotted in scan space; however, it is highly regular when plotted inphase space. In addition, when plotted in phase space, the Lissajouspattern forms a series of parallel lines, which, as they reach one sideof plot 802, wrap around to the other side. It should be noted that theslope of the parallel lines that manifest in phase space is directlyrelated to the frequency ratio.

FIGS. 9A-B depict a representative Lissajous pattern plotted in scanspace and phase space, respectively, where the Lissajous pattern isgenerated using drive signal having a frequency ratio of 7:11.

Plots 900 and 902 show a Lissajous scan overlaying an image of scanregion 206, plotted in scan space and phase space, respectively, wherethe Lissajous scan is generated with drive signals 218-1 and 218-2having a frequency ratio of 7:11.

For any pair of test frequencies f_(T) 1(i) and f_(T) 2(j), therelationship between their respective phases ψ₁(i) and ψ₂(j) at anytime, t, is given by the modulo equation:

ψ₂(j,t)=R(i,j)ψ₁(i,t) (mod 2π),

which can be evaluated at every full cycle of f_(T) 1(i) resonance(i.e., when ψ₁(i) is an integer multiple, p, of 2π) as:

ψ₂[p]=2πR(i,j)p (mod 2π).

Returning to method 600, at operation 608, the spatiotemporal scandensity, SD(i,j) for test scan pattern TSP(i,j) is determined. In someembodiments, the scan density of test scan pattern TSP(i,j) is definedas the largest modulo 2π distance, D_(max)(i,j), among pairs of scanlines adjacent in space, for a given finite sampling time.

It should be noted that is possible to recursively compute D_(max)(i,j).As a result, in some embodiments, it is not necessary to actuallygenerate a plot of a scan pattern in phase space to determine it andoperation 607 is optional.

For example, the distance, D_(↑), between the first scan line at t=0 andthe closest scan line above it after k periods, for f_(T) 1(i) and f_(T)2(j), can be expressed recursively as (temporarily neglecting the (i,j)notation for clarity):

  D_(↑)[0] = 2πD_(↑)[k] = min (D_(↑)[k − 1], mod (ψ₂[k], 2π)) = min (D_(↑)[k − 1], mod (2π Rk, 2π)) = min (D_(↑)[k − 1], 2π mod (Rk, 1)),

while the distance, D_(↓), between the first scan line and the adjacentscan line below it after k periods, can be expressed recursively as:

     D_(↓)[0] = 2πD_(↓)[k] = min (D_(↓)[k − 1], mod (−ψ₂[k], 2π)) = min (D_(↓)[k − 1], mod (−2π Rk, 2π)) = min (D_(↓)[k − 1], 2π mod (−Rk, 1)),

where the maximum gap size for test scan pattern TSP(i,j) at a givenscan cycle, k, is simply the maximum of the two single-sided gap sizes:

D _(max)(i,j)[k]=max(D _(↑)[k],D _(↓)[k]),

where D_(max)[k] represents the spatiotemporal density of TSP(i,j),since it describes how dense the scan is after each iteration, k, of aperiod of test drive frequency fT1(i).

At operation 609, the rate at which D_(max)(i,j) shrinks over time isdetermined. In some embodiments, this rate is determined by identifyinga baseline value that D_(max)(i,j) approaches after some number ofdrive-frequency cycles, and the number of cycles required to reach thisbaseline value.

FIG. 10 depicts a plot of D_(max)(i,j)[k] versus the number ofdrive-signal cycles, k, for a drive signal used to generate scanpatterns generated using two different sets of test frequencies. Plot1000 includes traces 1002 and 1004, which show the progression of thevalue of D_(max)(i,j) over successive periods of drive signal 218-1 fortest frequencies having 20:41 and 20:43 ratios, respectively. In someembodiments, the value of D_(max)(i,j) is plotted over successiveperiods of drive signal 218-2.

Each of traces 1002 and 1004 are characterized by the same baselinevalue BV, which is equal to approximately a/16 in the depicted example.However, the conversion time, τ2, for the test-frequency pair having aration of 20:43 (i.e., trace 1004) is significantly shorter than theconversion time, τ1, for the test-frequency pair having a ration of20:41 (i.e., trace 1002). For the purposes of this Specification,including the appended claims, “conversion time” is defined as the timerequired for the largest modulo 2π distance of a scan pattern to reach avalue that differs from its baseline value by less than a desiredoffset. In the depicted example, the desired offset is equal to π/25;however, any offset value can be used without departing from the scopeof the present disclosure.

Specifically, plot 1000 shows that the drive-frequency ratio of 20:43approaches baseline value BV in only 14 cycles of its test drivefrequency f_(T) 1, reaching this baseline value in only 28 cycles. Incontrast, the drive-frequency ratio of 20:41 requires 38 cycles of itsf_(T) 1 to approach BV and 39 cycles to reach its base value.Alternatively, in some embodiments, threshold value TV is used as ametric in place of baseline value BV, where TV is a user-defined valuefor any of a wide range of eye-tracker system attributes. This isparticularly advantageous when different drive-frequency ratios arecharacterized by different baseline values. In the depicted example,threshold value TV for a minimum acceptable spatial density foreye-tracking system 100.

In some embodiments, the suitability of a test-frequency pair isevaluated by determining the area under the trace of D_(max)(i,j) versussuccessive periods of one of drive signals 218-1 and 218-2. For example,in plot 1000, the area under trace 1004 is smaller than the area undertrace 1002; therefore, its drive-frequency ratio would typically beconsidered preferable to that used to generate trace 1002.

At operation 610, a test-frequency pair of the set of test-frequencypairs is selected as the drive frequencies of drive signals 218-1 and218-2 based on at least one of:

-   -   i. the values determined for spatiotemporal scan densities        SD(1,1) through SD(m,n); or    -   ii. the values of τ(1,1) through τ(m,n); or    -   iii. a plurality of data rates defined by the time for each of        spatiotemporal scan densities SD(1,1) through SD(m,n) to become        smaller than a user-selected feature size; or    -   iv. a plurality of data rates defined by the time for each of        spatiotemporal scan densities SD(1,1) through SD(m,n) to become        smaller than a user-selected threshold value; or    -   v. the values determined for spatiotemporal scan densities        SD(1,1) through SD(m,n) relative to a user-selected value for        D_(max); or    -   vi. the rate at which each of D_(max)(1,1) through D_(max)(m,n)        shrinks; or    -   vii. the area under the curve of a plot of D_(max) versus cycles        of one of test drive frequencies f_(T) 1 and f_(T) 2;    -   viii. any combination of i, ii, iii, iv, v, vi, and vii.

Although method 600 includes a specific order of method steps, the orderof the steps can differ from what is disclosed. Also, two or more stepscan be performed concurrently or with partial concurrence. Suchvariation will depend on the software and hardware systems chosen and ondesigner choice, among other factors. All such variations are within thescope of the disclosure. Likewise, software implementations could beaccomplished with standard programming techniques with rule-based logicand other logic to accomplish the various connection steps, calculationsteps, processing steps, comparison steps, and decision steps.

As noted briefly above, in some embodiments, photodetector module 202includes a non-imaging plurality of photodetectors that is configuredsuch that each photodetector can detect light reflected from scan region206. Such an arrangement is particularly advantageous, for example, whenreflected signal 210 is diffuse.

FIG. 11 depicts a schematic drawing of an alternative operationaleye-tracking geometry in accordance with the present disclosure. System1100 is analogous to system 100; however, system 1100 includesphotodetector module 1102, which comprises five photodetectors arrangedsuch that each photodetector can detect light reflected from scan region206. It should be noted that the plurality of photodetectors does notcollectively image scan region 206 since each is a non-imagingphotodetector and no wavefront information is contained in their outputsignals. Although the depicted example includes a photodetector modulehaving five photodetectors, any practical number of photodetectors canbe included in photodetector module 1102 without departing from thescope of the present disclosure.

In the depicted example, photodetector module 1102 includes at least onephotodetector having a gain configuration sufficient to enable it todetect a diffuse reflection from scan region 206 having a relativelylower level of light and still trigger a rising edge in its outputsignal. As light signal 202 traverses an iris-to-pupil edge, the diffusereflection vanishes and may produce a falling edge. In practice, thepolarity of the edges may be reversed, such that the pupil regionrepresents the “high” state of the photodiode output, while the irisregion represents the “low” state of the photodetector output.

FIG. 12 depicts a series of timing diagram plots illustrating scanningin phase lock/resonance based optical feedback according to aspects ofthe present disclosure.

Plot 1200 shows the timing of the pulses produced by the plurality ofphotodetectors in photodetector module 1102 with respect to the drivesignal to the MEMS device. Because of a second-order transfer functionof the MEMS device, a phase shift exists between drive signals 218-1 and218-2 and the mechanical position of the device. This phase offset mustbe considered in order to correlate timing of photodiode pulses with theangle of the MEMS device.

If the eye is stationary, the pulses captured by the system while thebeam sweeps in forwards and backwards in the horizontal direction willbe symmetric with respect to a first line of symmetry that representsthe phase offset of the horizontal actuator (e.g., actuator 404-1) at,or near, its resonant frequency. Additional phase delay may be producedby the thermal time constant of the actuators, which may beelectrothermal devices. Similarly, as the beam sweeps upwards anddownwards in the vertical direction, a second line of symmetryrepresenting the phase offset of the vertical actuator (e.g., actuator404-2) will arise. Because the actuators are orthogonal, the verticaland horizontal phase offsets can be calculated independently.

In some embodiments, the phase offset for at least one of the verticaland horizontal axes is calculated by autoconvolution, in which thecorneal reflection magnitude (e.g., as shown in FIG. 12) is convolvedwith itself. The output of such an autoconvolution will typicallycontain a maximum at the line of symmetry, revealing the phase offset.It should be noted that autoconvolution can be performed independentlyfor each of the vertical and horizontal axes.

In some embodiments, in 2 dimensions, a circular convolution of thephase space representations (e.g., as shown in FIGS. 8B and 9B) wouldreveal lines of symmetry for each of the vertical and horizontal axes.

It should be noted that such operations can be used in any embodiment inaccordance with the present disclosure to calculate the phase offsets ofscanner 110 without requiring integrated position sensors.

FIG. 13 depicts a plot of the detected pulses from photodetector module1102. Plot 1300 includes output signals from each photodetector in thephotodetector module. With the phase offsets calculated and drivefrequencies selected to substantially optimize the surface area coverageof scan region 206, the output signals collectively define a point cloudthat reveals five corneal glint contours and one pupil outline per eye.It should be noted that a glint may appear to stretch out as ittransitions from the corneal region to a scleral region upon rotation ofthe eye, after which it may no longer be present. Furthermore, it isimportant to note that, like system 100, system 1100 is a “non-imaging”system since no wavefront information is contained in any of the outputsof the photodetectors of photodetector module 1102; therefore, no imageprocessing algorithms or streaming video from a camera are required tocapture these point clouds at high data rates.

The positions of pulses that form contours of glints may be furtherprocessed to calculate the centroid position of the glints. A commoncentroid calculation may be performed, but this technique may not be asefficient as other methods based on the geometry of the glint data. Forexample, the perpendicular bisector of at least 2 chords of the glintcircle may be used to capture the center position with fewer datapoints,resulting in lower latency and higher bandwidth.

FIG. 14 shows a representation of the corneal glints as single points,as well as time series data corresponding to the pulses. Plot 1400 isgenerated using the operations described above and with respect to FIG.13 on the raw point cloud data. In addition, multiple glints are used tocompute the position of a “fused” glint, which may be calculated basedon some knowledge of the photodetector placement within the eye trackingsystem. The fused glint position is estimated from however many glintsare present for a given eye angle (at least 2), thereby improving therobustness of the system.

FIG. 15 depicts estimation of a gaze angle based on fused glintpositions. Plot 1500 is representative of an estimate generated after acalibration is performed, which relates real-world gaze angles to glintpositions. It should be noted that small changes in the system geometry(e.g. from glasses shifting on a user's face) can give rise to largedeviations in the estimated gaze angle.

FIG. 16 depicts pupil information and related glint information obtainedin accordance with the present disclosure. Plot 1600 shows pupil shapesextracted from point clouds while rejecting noise via the operationsdescribed above.

It is an aspect of the present disclosure that the availability of bothpupil and glint information enables slip-invariant eye tracking, whichcan be achieved via any of a range of suitable techniques, such aspupil-center corneal reflection (PCCR) methods. In PCCR, a vector fromthe pupil center to the fused glint is captured, and calibration of thisvector to real-world gaze angles is performed by a given user (one-timecalibration). Subsequent sessions may re-use this calibration forconvenience and ease-of-use.

It is a further aspect of the present disclosure that a calibrated andslip invariant eye tracker can function as a human-computer-interfacedevice. When considering the design of such an interface, it isimportant to suppress unintentional eye movements which occur constantlyas a user explores their visual field. It is also important to minimizeeye strain through the use of intuitive eye-based gestures that do notrequire a user to constrain their gaze to signal inputs.

FIG. 17 depicts an example of an eye-tracker-basedhuman-computer-interface in accordance with the present disclosure.Display 1700 includes a video displays 1702-1 through 1702-36, which arearranged in a 4×9 array. System 1200 is employed as ahuman-computer-interface that determines the gaze direction of a user,which, in this example, is directed at display 1702-34. As a result, allof the televisions are put in an “off” mode except for display 1702-34.In other words, each of video displays 1702-1 through 1702-36 is“selected” or “unselected” based upon the gaze direction of the user asdetermined by system 1200.

As will be apparent to one skilled in the art, eye-tracking systems inaccordance with the present disclosure can be used as ahuman-computer-interface in myriad ways. In some embodiments, system1200 can be used to navigate a menu by, for example:

-   -   blinking to start a navigation application; or    -   scrolling icons along a display by looking towards one side of        the navigation pane; or    -   stopping icon scroll by pursuing an icon; or    -   double blinking to select the icon of interest; or    -   any combination of the above.

Scrolling objects, which are extensively used in applications on mobilehandsets and smart glasses due to their limited screen real-estate,often trigger the Optokinetic Reflex (OKR), which is characterized by aseries of alternating smooth pursuit and saccade eye movements.

Embodiments in accordance with the present disclosure are capable ofextremely high rates of eye tracking because no image processing isrequired. As a result, they are able to derive knowledge of the dynamicsof eye movements and the durations of smooth pursuit movements, whichcan be used to detect a user's level of interest in scrolling content.As a result, the user may effortlessly decelerate scrolling objects toland on an object of interest. Although the use of blinks as an inputgesture may result in false positives, the high sampling rate attainablethrough the teachings provided herein can be used to set timingthresholds to disambiguate involuntary blinks, which have consistentdurations that relate to a user's state (e.g. fatigue) from intentionalblinks.

FIG. 18 depicts another eye-tracking-based user interface example inaccordance with the present disclosure. Plot 1800 is a representation ofa fruit slicing application in which, when a user looks towards anobject to be sliced, the direction of the user's saccade is used toslice all objects along the saccade vector.

In some embodiments, the slicing vector extends beyond the fixation ofthe user by an amount that may be set by the peak velocity of thesaccade, by the reaction time of the user to the presence of the object,or by some other means. Since the use of a saccade without any means ofconfirming intent can give rise to false positives, in some embodiments,a separate input mechanism (e.g. keystroke, mouse click, head gesture asmeasured by an inertial measurement unit (IMU), etc.) is used to triggeran action.

FIG. 19 depicts yet another graphical-user interface that can be used toconfigure an avatar. As depicted in plot 1900, when a user looks at the“scroll” regions, objects appear from the direction of their gaze andscroll away from the scroll target. Once a property of the avatar isselected by a short fixation, it is highlighted. In some embodiments, asubsequent saccade towards the avatar then causes the avatar to inheritthe property. In some embodiments, the direction and magnitude of thesaccade (which can be calculated even in the presence of errors inaccuracy) are used to trigger a change in an avatar (even when havingmultiple avatars).

Furthermore, as disclosed in U.S. Non-Provisional patent applicationSer. No. 15/876,148 (now U.S. Pat. No. 10,824,229), which isincorporated herein by reference, embodiments in accordance with thepresent disclosure enable saccade endpoint prediction based on detectionof saccade dynamics. Such endpoint prediction can be used to increasethe responsiveness of the user interface. In particular, since itenables the user interface to react even faster than the user's gaze, itis important to highlight the changes until the user's fixation settleson the target object.

It should be noted that other forms of feedback can also be used, suchas auditory feedback upon selection or visual feedbacks in the peripheryor along the saccade direction during the saccade. In addition, theability to undo actions should be simple, and the undone actions mayalso be highlighted until the user's fixation returns to the avatar. Inplot 1900, the categories of properties may also be selected using asimilar scrolling and selecting process. It is important to note thatthese methods of signaling interest and intent through natural eyemovements are not limited to objects inheriting properties, analogous to“drag and drop” actions that may be performed with a mouse or acapacitive touch interface.

In addition, the use of multimodal gestural inputs may be used toimprove the robustness of actions in a user interface. For example, aVOR (vestibulo-ocular reflex) eye movement, which occurs when the eyefixates a target while the head is rotating, may be robustly captured bycomparing IMU data to counter-rotation of the eye. A VOR in a givendirection, combined with gaze position, may be used to implementswiping, pinch-to-zoom, pan, etc.

It should be further noted that, when implementing a blink-based inputmethod, the target region may be highlighted when the users gaze is onit to indicate that a blink will trigger action. This highlight, amongother potential cues (e.g., sound, vibration, etc.) may providesufficient feedback to the user to suppress blinks in order to avoidfalse selections. In addition, the nature of the cue may be used tospecify the type of action that would be triggered (e.g., select, back,undo, pan, zoom, etc.).

The construction and arrangement of the systems and methods as shown inthe various exemplary embodiments are illustrative only. Although only afew embodiments have been described in detail in this disclosure, manymodifications are possible (e.g., variations in sizes, dimensions,structures, shapes and proportions of the various elements, values ofparameters, mounting arrangements, use of materials, colors,orientations, etc.). For example, the position of elements can bereversed or otherwise varied and the nature or number of discreteelements or positions can be altered or varied. Accordingly, all suchmodifications are intended to be included within the scope of thepresent disclosure. The order or sequence of any process or method stepscan be varied or re-sequenced according to alternative embodiments.Other substitutions, modifications, changes, and omissions can be madein the design, operating conditions and arrangement of the exemplaryembodiments without departing from the scope of the present disclosure.

It is to be understood that the disclosure teaches just some examples ofillustrative embodiments and that many variations of the invention canbe devised by those skilled in the art, after reading this disclosure,and that the scope of the present invention is to be determined by thefollowing claims.

What is claimed is:
 1. An eye-tracking method comprising: identifying afirst location of a cornea of an eye, the cornea having a cornealsurface; scanning a light signal in scan pattern over a region of theeye through the effect of a microelectromechanical system (MEMS) devicethat is a two-axis device having a first axis characterized by a firstresonant frequency and a second axis characterized by a second resonantfrequency, wherein the scan pattern is a Lissajous pattern, and whereinthe light signal is scanned by driving the first axis with a firstperiodic signal having a first drive frequency and driving the secondaxis with a second periodic signal having a second drive frequency;detecting a reflected signal from the corneal surface with a non-imagingphotodetector configuration; and identifying a gaze direction for theeye based on the reflected signal.
 2. The method of claim 1 wherein theratio of the first and second drive frequencies is 2:1.
 3. The method ofclaim 1 wherein the ratio of the first and second drive frequencies is arational number.
 4. The method of claim 1 further comprising selectingfirst and second drive frequencies that give rise to precession of theLissajous pattern.
 5. The method of claim 1 further comprisingdetermining the first and second resonant frequencies.
 6. The method ofclaim 1 further comprising providing the non-imaging photodetectorconfiguration such that it includes a plurality of non-imagingphotodetectors.
 7. The method of claim 1 further comprising: determininga spatiotemporal scan density for each of a plurality of scan patterns,wherein each scan pattern is based on the first periodic signal having adifferent first test frequency of a set thereof and the second periodicsignal having a different second test frequency of a set thereof;wherein each of the set of first test frequencies is based on the firstresonant frequency and a first offset frequency; and wherein each of theset of second test frequencies is based on the second resonant frequencyand a second offset frequency.
 8. The method of claim 7 furthercomprising selecting the first and second drive frequencies based on theplurality of spatiotemporal scan densities.
 9. The method of claim 8wherein the first and second drive frequencies are selected as thefrequency pair that results in the highest spatiotemporal scan density.10. The method of claim 7 wherein the spatiotemporal scan density foreach test scan pattern is determined by operations including: for aplurality of periods of the first test frequency, plotting the test scanpattern in phase space as a plurality of parallel scan lines;determining a plurality of separations, each separation being thedistance between a different pair of adjacent parallel scan lines; anddetermining a largest separation of the plurality thereof.
 11. Themethod of claim 10 further comprising: for each of the plurality of testscan patterns: (i) determining a baseline value for the largestseparation; and (ii) computing a conversion time, wherein the conversiontime is based on the number of periods of the first test frequencyrequired for the largest separation to reach the baseline value; andselecting the first and second drive frequencies based on at least oneof (1) the plurality of spatiotemporal scan densities and (2) theplurality of conversion times.
 12. An eye tracker comprising: a lightsource for providing a light signal; a scanner for steering the lightsignal in a Lissajous pattern over a region of an eye, wherein thescanner comprises a micromechanical system (MEMS) device that is atwo-axis device having a first axis characterized by a first resonantfrequency and a second axis characterized by a second resonantfrequency; a non-imaging photodetector configuration that is configuredto provide at least one output signal based on a reflected signal fromthe region; and a processing system configured to: (i) drive the firstaxis with a first periodic signal that is characterized by a first drivefrequency; (ii) drive the second axis with a second periodic signal thatis characterized by a second drive frequency; and (iii) determine a gazedirection of the eye based on the output signal.
 13. The eye tracker ofclaim 12 wherein the ratio of the first and second drive frequencies is2:1.
 14. The eye tracker of claim 12 wherein the ratio of the first andsecond drive frequencies is a rational number.
 15. The eye tracker ofclaim 12 wherein the first and second drive frequencies give rise to aprecession of the Lissajous pattern.
 16. The eye tracker of claim 12wherein non-imaging photodetector configuration includes a plurality ofnon-imaging photodetectors.
 17. The eye tracker of claim 12 wherein theprocessor is further configured to: (iv) determine a spatiotemporal scandensity for each of a plurality of scan patterns, wherein each scanpattern is based on the first periodic signal having a different firsttest frequency of a set thereof and the second periodic signal having adifferent second test frequency of a set thereof; wherein each of theset of first test frequencies is based on the first resonant frequencyand a first offset frequency; and wherein each of the set of second testfrequencies is based on the second resonant frequency and a secondoffset frequency.
 18. The eye tracker of claim 17 wherein the processoris further configured to (v) select the first and second drivefrequencies based on the plurality of spatiotemporal scan densities. 19.The eye tracker of claim 17 wherein the processor is further configuredto, for each of the plurality of test scan patterns: (v) for a pluralityof periods of the first test frequency, plot the test scan pattern inphase space as a plurality of parallel scan lines; and (vi) determine aplurality of separations, each separation being the distance between adifferent pair of adjacent parallel scan lines; and (vii) determine alargest separation of the plurality of separations.
 20. The eye trackerof claim 19 wherein the processor is further configured to: (viii)determine a baseline value for the largest separation for each of theplurality of test patterns; (ix) compute a conversion time for each ofthe plurality of test patterns, wherein the conversion time is based onthe number of periods of the first test frequency required for thelargest separation to reach the baseline value; and (x) select the firstand second drive frequencies based on the plurality of conversion times.